I have AMD Athlon II x4 I'm fine with.
current motherboard has AM3 socket with AMD 770 chipset, and I ponder to get new MB with AM3+ socket and AMD 970 chipset.

CPU upgrade isn't an option now. because of obsolete socket I couldn't install new CPU on current MB, but 970 one has AM3+ socket which can still be used for CPUs newer that mine, like FX series.

but I wonder, is this change worth the trouble at all, considering that newer one is already 7 years old?

Don't. You'd waste money for an "upgrade" from one obsolete build to the next when the same kind of money would allow you to upgrade to a current mid-range mainboard and CPU.

Absolutely no. Save your money for a Ryzen CPU and a AM4 socket motherboard.

thank you for the answers!